Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void DcFilter(double TransitionBandwidth, double FS, TVec *Num, TVec *Den); | Design a DC filter. |
| 2 | void DcFilter(double alpha, TVec *Num, TVec *Den); | Design a DC-blocking (high-pass) IIR filter from alpha. |
| 3 | double DcFilter(double NewValue, TCplx &State, double alpha = 0.99); | State parameter holds the filter state. |
Overload 1: void DcFilter(double TransitionBandwidth, double FS, TVec *Num, TVec *Den);
Design a DC filter.
Design a DC filter with TransitionBandwidth and place the transfer function in Num (numerator) and Den (denominator). You can then use this transfer function to initialize an IIR filter with a call to IirInit.
A DC filtered signal will be centered around zero. This DC filter is a simple differentiator/integrator pair. Transition bandwidth is the width of the frequency band where the amplitude is not yet completely attenuated. With DC filters, the transition band starts at 0 Hz. Narrow transition band (TransitionBandwidth/FS ratio is small) will result in filters with longer delays. FS is the sampling frequency. The filter implements the following difference equation:
y[i] = x[i] - x[i-1] + alpha y[i-1]
x.. input signal y.. output signal alpha.. parameter
Alpha paremeter can control the 3dB frequency of the transition bandwidth:
alpha := 1-(TransitionBandwidth/FS)*Pi;
FS.. sampling frequency
TransitionBandwidth.. frequency up to which will the filter have more
then 3dB attenuation. Must be less then FS/2.Overload 2: void DcFilter(double alpha, TVec *Num, TVec *Den);
Design a DC-blocking (high-pass) IIR filter from alpha.
Builds the transfer function of a first-order DC blocker and stores it in num / den for use with IirInit / IirFilter; the filtered signal is centred around zero (its mean is removed). With unity-DC-gain correction g = alpha/big(alpha + 1/2(1-alpha)big) the filter is
H(z) = g (1 - z^(-1))/(1 - alpha z^(-1))
i.e. a differentiator/integrator pair with a zero at z=1 (DC) and a pole at z=alpha. Domain: 0 < alpha < 1 (typically 0.99-0.9999); alpha nearer 1 pushes the cut-off lower and lengthens the transient. A finite alpha in range yields finite coefficients.
#include "MtxExpr.h"
#include "Units.SignalUtils.h"
using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Signal;
using namespace Dew::Signal::Units::SignalUtils;
void Example()
{
Vector b, c, Response, num, den, X;
int n, i;
TIirState IirState;
TCplx DCState;
Tone(b, 300, 5.0/300, 0, 1); //generate sine with 5 periods in 300 samples
// Alternative:
// b.RandGauss();
b = b + 2;
c.Copy(b);
n = 10;
DcFilter(0.95, num, den);
IirInit(num, den, IirState);
int bLength = b.Length;
for (i = 0; i <= bLength / n - 1; i++) //only to test the streaming
{
b.SetSubRange(i*n, n);
c.SetSubRange(i*n, n);
IirFilter(b, c, IirState);
}
b.SetFullRange();
c.SetFullRange();
FrequencyResponse(num, den, Response, 64);
DcFilter(0.05, 2, num, den);
IirInit(num, den, IirState);
bLength = b.Length;
for (i = 0; i <= bLength / n - 1; i++) // the loop is only to test the streaming
{
b.SetSubRange(i*n, n);
c.SetSubRange(i*n, n);
IirFilter(b, c, IirState);
}
b.SetFullRange();
c.SetFullRange();
FrequencyResponse(num, den, Response, 64);
DCState = C_ZERO;
for (i = 0; i <= b.Length - 1; i++)
c.Values(i) = DcFilter(b.Values(i), DCState, 0.95);
}Overload 3: double DcFilter(double NewValue, TCplx &State, double alpha = 0.99);
State parameter holds the filter state.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NewValue | double | |
| 2 | State | TCplx & | |
| 3 | alpha = 0.99 | double |
NewValue is the next sample and alpha is typically between 0.99 and 0.9999 and must be < 1. Big alpha will cause longer filter delay and more ringing. State should be initialized to zero before the routine is called for the first time.
#include "MtxExpr.h"
#include "Units.SignalUtils.h"
using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Signal;
using namespace Dew::Signal::Units::SignalUtils;
void Example()
{
Vector b(0);
Vector c(0);
Vector num(0);
Vector x(0);
Vector den(0);
Vector Response(0);
int n;
int i;
TIirState IirState;
TCplx DCState;
Tone(b, 300, 5.0/300, 0, 1, false); //generate sine with 5 periods in 300 samples
// Alternative:
// b.RandGauss();
b = b + 2;
c.Copy(b);
n = 10;
DcFilter(0.95, num, den);
IirInit(num, den, IirState, false);
int bLength = b.Length;
for (i = 0; i < (bLength/n); i++) //only to test the streaming
{
b.SetSubRange(i*n, n);
c.SetSubRange(i*n, n);
IirFilter(b, c, IirState);
}
b.SetFullRange();
c.SetFullRange();
FrequencyResponse(num, den, Response, 64, false, TSignalWindowType::wtRectangular, 0);
DcFilter(0.05, 2, num, den);
IirInit(num, den, IirState, false);
bLength = b.Length;
for (i = 0; i < (bLength/n); i++) //only to test the streaming
{
b.SetSubRange(i*n, n);
c.SetSubRange(i*n, n);
IirFilter(b, c, IirState);
}
b.SetFullRange();
c.SetFullRange();
FrequencyResponse(num, den, Response, 64, false, TSignalWindowType::wtRectangular, 0);
DCState = C_ZERO;
for (i = 0; i < (b.Length); i++) //only to test the streaming
{
c.Values(i) = DcFilter(b.Values(i), DCState, 0.95);
}
}